{"paper":{"title":"Modular Forms and Calabi-Yau Varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Dinakar Ramakrishnan, Kapil Paranjape","submitted_at":"2014-04-04T05:22:36Z","abstract_excerpt":"Given a holomorphic newform $f$ of weight $k$ and with rational coefficients, a question of Mazur and van Straten asks if there is an associated Calabi-Yau variety $X$ over ${\\mathbb Q}$ of dimension $k-1$ such that the $\\ell$-adic Galois representation of $f$ occurs in the cohomology of $X$ in degree $k-1$. We provide some explicit examples giving a positive answer, and show moreover that such $X$ come equipped with an involution $\\tau$ acting by $-1$ on $H^0(X, \\Omega^{k-1})$. We also raise a general question regarding the regular algebraic, (essentially) selfdual cusp forms $\\pi$ on GL$(n)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1154","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}